Final answer:
Using the quadratic formula to solve the equation -2x² - 16x - 44 = 0, we find that there are two complex solutions. The correct solutions are x = -4 ± 4i√6. The correct answer is not one of the provided options.
Step-by-step explanation:
To solve the quadratic equation -2x² - 16x - 44 = 0, we can use the quadratic formula which is given by -b ± √b² - 4ac over 2a. In this case, a = -2, b = -16, and c = -44. Substituting these values into the quadratic formula we get:
x = √(-16)² - 4(-2)(-44) over 2(-2)
After simplifying, we obtain:
x = 16 ± √(256 - 352) over -4
x = 16 ± √(-96) over -4
Since the discriminant (the value inside the square root) is negative, we have no real solutions and two complex solutions. The final solutions have the form:
x = 16 ± 4i√6 over -4
Therefore, the solutions are x = -4 ± 4i√6. This corresponds to option (c) x = 4i√6, but with the correct sign, making option (c) incorrect. The correct answer, accounting for the sign, is not listed among the options provided by the student.